Stabilising terminal cost and terminal controller for ℓ&lt;inf&gt;asso&lt;/inf&gt;-MPC: enhanced optimality and region of attraction

Gallieri, Marco; Maciejowski, Jan M.

doi:10.23919/ecc.2013.6669549

Cited by 10 publications

(14 citation statements)

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“…However, MPC with a quadratic cost function will tend to lead to long periods of relatively low and continuous thrust, whereas for a system propelled by gas thrusters, a degree of sparsity in the control actions is preferable. Such behaviour can be achieved by combining the quadratic cost with an additional ℓ 1 term on the input, , informally dubbed as ℓ asso ‐MPC in homage to the least absolute shrinkage and selection operator used in regularised least‐squares regression. MPC with this class of cost function has been demonstrated for the terminal phases of spacecraft rendezvous in circular orbits in .…”

Section: Background and Design Motivationsmentioning

confidence: 99%

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Hartley

Maciejowski

2014

Optim Control Appl Methods

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A field programmable gate array (FPGA) based model predictive controller for two phases of spacecraft rendezvous is presented. Linear time-varying prediction models are used to accommodate elliptical orbits, and a variable prediction horizon is used to facilitate finite time completion of the longer range manoeuvres, whilst a fixed and receding prediction horizon is used for fine-grained tracking at close range. The resulting constrained optimisation problems are solved using a primal-dual interior point algorithm. The majority of the computational demand is in solving a system of simultaneous linear equations at each iteration of this algorithm. To accelerate these operations, a custom circuit is implemented, using a combination of Mathworks HDL Coder and Xilinx System Generator for DSP, and used as a peripheral to a MicroBlaze softcore processor on the FPGA, on which the remainder of the system is implemented. Certain logic that can be hard-coded for fixed sized problems is implemented to be configurable online, in order to accommodate the varying problem sizes associated with the variable prediction horizon. The system is demonstrated in closed-loop by linking the FPGA with a simulation of the spacecraft dynamics running in Simulink on a PC, using Ethernet. Timing comparisons indicate that the custom implementation is substantially faster than pure embedded software-based interior point methods running on the same MicroBlaze and could be competitive with a pure custom hardware implementation.During the impulsive phase, the control objective is to guide the chaser towards the vicinity of the target via a sequence of predetermined 'holding points' at which it must remain pending clearance to continue (Figure 1(b)). Such trajectories are often informally described as hopping, because in the ideal case (without any parametric or additive uncertainties), they comprise impulsive inputs at the start and finish separated by a long period of free drift. In the present scenario, the holding Recently, interest has arisen in using FPGAs to exploit opportunities for parallelism in the numerical algorithms used to implement MPC, with a variety of approaches proposed. A hybrid softwarehardware design is advocated by [32][33][34]. The first uses a primal barrier method, and the custom accelerator is used to calculate the gradient vector and Hessian matrix of the augmented cost function at each iteration, whilst the latter two use an active set method, with a custom circuit expediting At a high level, the custom PCORE is split into two major parts. The first component performs steps 6-8 and 10 of the Algorithm in Figure 2(a), building the linear system, whilst the second more complex component performs step 9.

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Section: Background and Design Motivationsmentioning

confidence: 99%

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Hartley

Maciejowski

2014

Optim Control Appl Methods

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“…The proposed selftriggered control law possesses three important features: (i) significant reductions in resource utilization are obtained, (ii) a priori closed-loop performance guarantees are provided (by design) in terms of the original cost function, next to asymptotic stability and constraint satisfaction, (iii) co-design of both the feedback law and triggering condition is achieved. To elaborate on these features, we emphasize that the proposed STC approach reduces resource utilization without modifying the cost function by input regularization or explicitly penalizing resource usage, thereby being essentially different from [3,[7][8][9][10]32]. This feature enables that the proposed STC strategy will not only realize stabilization towards a desired equilibrium, but it also provides a priori guarantees on an infinite horizon cost directly related to the MPC cost (feature (ii)).…”

Section: Introductionmentioning

confidence: 96%

“…The most well known approach is based on modifying the MPC problem by appending the original MPC control cost with an ℓ 1 penalty on the input in order to obtain sparse input signals. Regularizing by the ℓ 1 -norm is known to induce sparsity in the sense that, individual components of the input signal will be equal to zero, see, e.g., [3,[7][8][9], in which the focus is on discrete-time linear systems. Also different types of sum-of-norms regularization can be used to obtain so-called group sparsity, meaning that at many http://dx.doi.org/10.1016/j.sysconle.2015.03.003 0167-6911/© 2015 Elsevier B.V. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach

Gommans

Heemels

2015

Systems & Control Letters

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“…However, explicitly including 0 -norm constraints in the control decision problem leads to an NP-hard combinatorial problem [15]. Mainly, three approaches have been proposed in optimal control problems to avoid the computational burden: i) a greedy algorithm known as Orthogonal Matching Pursuit (OMP) [5], ii) a 1 -norm relaxation [3], [16] and more recently iii) an algorithm based on coordinate descent type methods [17].…”

Section: Introductionmentioning

confidence: 99%

“…Works such as [4], [7], [16] and [5] have introduced sparsity constraints on the control inputs when dealing with model predictive control (MPC). While in [4], [7], [16] the authors also included extra convex constraints in the optimization problem, in [5] this issue is not clearly established. Still, neither of them consider 0 -norm restrictions to limit the number of active control actions at each control horizon instant.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Model Predictive Control Including Input Cardinality Constraints

Aguilera

Urrutia

Delgado

et al. 2017

IEEE Trans. Automat. Contr.

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This note addresses the problem of feedback control with a constrained number of active inputs. This problem is known as sparse control. Specifically, we describe a novel quadratic model predictive control strategy that guarantees sparsity by bounding directly the 0-norm of the control input vector at each control horizon instant. Besides this sparsity constraint, bounded constraints are also imposed on both control input and system state. Under this scenario, we provide sufficient conditions for guaranteeing practical stability of the closed-loop. We transform the combinatorial optimization problem into an equivalent optimization problem that does not consider relaxation in the cardinality constraints. The equivalent optimization problem can be solved utilizing standard non-linear programming toolboxes that provides the input control sequence corresponding to the global optimum.

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Stabilising terminal cost and terminal controller for ℓ<inf>asso</inf>-MPC: enhanced optimality and region of attraction

Cited by 10 publications

References 0 publications

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Field programmable gate array based predictive control system for spacecraft rendezvous in elliptical orbits

Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach

Quadratic Model Predictive Control Including Input Cardinality Constraints

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